Raster input scanner (RIS) systems are frequently employed in electrophotographic copiers and facsimile machines. Typically, a raster input scanner comprises an elongated array of photosensors mounted in optical alignment with a lens or lens array. In operation, light reflected from an image-bearing member is captured by the lens or lens array and focused onto the photosensors. The photosensors sense the reflected light and produce outputs that are sent to other systems for amplification, storage, display, reproduction, or manipulation.
While various types of raster input scanners are known, one such type uses a lens array comprised of bundled gradient index optical fibers or rods. Reference U.S. Pat. No. 3,658,407, issued Apr. 25, 1972 to Ichiro Kitano et al. for a description of light conducting rods that have a cross sectional refractive index distribution that varies parabolically outward from a center portion. Those rods can act as focusing lenses for light captured at one end. Such lenses are produced under the trade name "SELFOC;" a name which is owned by Nippon Sheet Glass Company, Ltd. Relevant optical characteristics of gradient index lens arrays are described in an article entitled "Optical properties of GRIN fiber lens arrays: dependence on fiber length", by William Lama, Applied Optics, Aug. 1, 1982, VoL 21, No. 15, pages 2739-2746.
To form a raster input scanner, a gradient index lens array is disposed between a photosensor array and the portion of an image-bearing surface illuminated by a light source. Light reflected by that surface is captured by the gradient index lenses and focused onto the photosensor.
In most such imaging applications it is important that the gradient index lenses have an adequate depth of focus. Otherwise, small changes in the relative positions of the gradient index lenses and the surface being scanned will cause relatively large changes in image quality. Indeed, it is usually desirable that the depth of focus of a gradient index array be as large as possible while meeting the radiometric efficiency requirements.
FIG. 1 is useful in explaining several important concepts. The illustrated conventional spherical lens L1 has an exit pupil diameter D.sub.1, a focal length FL, and a depth of focus DOF. The relative aperture or f/# of lens L1 is the focal length FL divided by the diameter of the exit pupil, or: EQU f/#=FL/D.sub.1.
As is well known, the depth of focus of a conventional lens can be increased (within limits imposed by the diffraction of light by the lens aperture) by increasing its relative aperture (or f/#). It is also well known that an increase in the depth of focus, when achieved by increasing f/#, results in a reduced radiometric efficiency (ratio of image irradiance to object radiance) and thus in the scanner's signal to noise ratio. Two relationships explain the trade-off of an increase in the depth of focus and a reduction in radiometric efficiency for conventional lenses. First, the radiometric efficiency is inversely proportional to (f/#).sup.2 =(FL/D.sub.1).sup.2. Second, the depth of focus (within limits previously described) is directly proportional to the f/#. For example, the f/# and thus the depth of focus (DOF) of the lens L2 of FIG. 2 is greater than that of the depth of focus of the lens L1 since the lens L2 has a smaller exit pupil diameter D.sub.2. This is true even though the focal lengths (FL) of lenses L1 and L2 are the same. However, since the radiometric efficiency is inversely proportional to (f/#).sup.2 =(FL/D).sup.2, the radiometric efficiency for the lens L2 is less than that of the lens L1.
Simply put, while the depth of focus of a lens can be increased by increasing the relative aperture (f/#), the price to be paid is a loss in radiometric efficiency. Likewise, radiometric efficiency can be increased by reducing the relative aperture (f/#), but only with a reduction in the depth of focus.
However, for gradient index lenses it can be shown that the radiometric efficiency is proportional to (n.sub.o A.times.R).sup.2, where n.sub.o is the axial refractive index of the optical rods, A is a constant which depends upon the gradient index of the lens, and R is the radius of the rods. It also can be shown that the depth of focus of a gradient index lens is inversely proportional to n.sub.o A.times.R. Thus a tradeoff between radiometric efficiency and depth of focus can be achieved using the glass properties, (n.sub.o, A), the glass rod radius, R, or both.
Given the trade-off between radiometric efficiency and depth of focus it is possible to select a good compromise for many applications. For example, in applications where an image bearing surface is accurately located with respect to the gradient index lens array, such as when single sheets of paper are placed on a flat platen and then scanned, having a relatively narrow depth of focus is acceptable and radiometric efficiency can be optimized. However, in some applications the surfaces being imaged cannot be accurately located. For example, when scanning a bound book on a flat platen the physical location of the book's page(s) may vary with respect to the gradient index lens array. In such applications having a wide depth of focus is beneficial, even if the radiometric efficiency is reduced.
However, in prior art gradient index array based imaging systems a single tradeoff has to be made. As indicated above, any single tradeoff is not optimal for all conditions. Therefore, a technique which enables imaging with gradient index lens arrays having different depths of focus would be advantageous.